### $mathbb{Z}_2$-homology of weak $(p-2)$-faceless $p$-pseudomanifolds may be computed in $O(n)$ time

#### Abstract

We consider the class of weak $(p-2)$-faceless $p$-pseudomanifolds

with bounded boundaries and coboundaries.

We show that in this class the Betti numbers with $\mathbb{Z}_2$ coefficients

may be computed in time $O(n)$ and the $\mathbb{Z}_2$ homology generators

in time $O(nm)$ where $n$ denotes

the cardinality of the $p$-pseudomanifold on input and

$m$ is the number of homology generators.

with bounded boundaries and coboundaries.

We show that in this class the Betti numbers with $\mathbb{Z}_2$ coefficients

may be computed in time $O(n)$ and the $\mathbb{Z}_2$ homology generators

in time $O(nm)$ where $n$ denotes

the cardinality of the $p$-pseudomanifold on input and

$m$ is the number of homology generators.

#### Keywords

Homology algorithm; Betti numbers; homology generators; 2-manifolds

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